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ABOUT ME

I am a PhD candidate in mathematics at the University of Nebraska-Lincoln. My advisor is Dr. Petronela Radu. I received my MS in mathematics from UNL in 2015, and my BS in applied mathematics from Brigham Young University-Idaho in 2013. When I am not doing math, I enjoy hiking, racquetball, board games, and good food. The picture above was taken at the top of Mt. Timpanogos in Utah, where I am originally from.

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RESEARCH

My research is in partial-integro differential equations. Specifically I work on models in the nonlocal framework of peridymamics. Peridynamics unifies the mechanics of continuous, discontinuous, and discrete material in one set of equations. It has been shown to be successful in tracking dynamics fracture in a variety of situations (tearing, cracking, bursting, corrosion etc.). I have introduced a new nonlocal Laplacian that arises naturally in the state-based theory of peridynamics, and have been studying its properties, such as convergence to the classical Laplacian.

This summer (2017) I had the opportunity to work at Oak Ridge National Laboratory for 10 weeks under the mentorship of Dr. Pablo Seleson. While there I worked on the analysis and simulation (in MATLAB) of coupled local/nonlocal models. In particular we used Peridynamics as our nonlocal framework. The work was funded by the NSF Mathematical Sciences Graduate Internship.  

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PUBLICATIONS

  • Radu, P., & Wells, K.(Submitted). A doubly nonlocal Laplace operator and its connection to the classical Laplacian. 

  • Radu, P., & Wells, K. (In progress). Convergence analysis for state-based Laplacian in bounded and unbounded domains.

  • Lai Y., Smith W., Wakefield N., Miller E., St. Goar J., Groothius C., Wells K. (2017). Characterizing Mathematics Graduate Student Teaching Assistants’ Opportunities to Learn from Teaching in Dewer J., Hus S., Pollatsek H. (Ed.), Mathematics Education, A Spectrum of Work in Mathematical Sciences Departments, Vol. 7 Springer.

  • Fredette, E., Kubala, D., Nelson, E., Wells, K., & Ellingsen, H. (2015). Growth functions of finitely generated algebras. Involve, a Journal of Mathematics Involve, 8(1), 71-74.

RESEARCH INTERESTS

Parital-integro differential equations, integral equations, partial differential equation, nonlocal calculus, continuum mechanics, computational mathematics, mathematical knowledge for teaching.

TEACHING

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INSTRUCTOR OF RECORD

  • Intermediate Algebra (Math 100A)

  • College Algebra (Math 101)

  • College Algebra & Trigonometry (Math 103)

  • Mathematics Matters (Math 300, for elementary education majors) 

  • Math Modeling (Math 302, for elementary education majors)

TEACHING ASSISTANT

  • Applied Calculus (Math 104)

  • Calculus I (Math 106)

  • Calculus II (Math 107)

  • Nebraska Math: Number, Geometry and Algebraic Thinking II for K-3 Math Specialists (Math 802p)

CURRICULUM WORK

I developed active learning workbooks for all sections of Math 100a.

“And so, does the destination matter? Or is it the path we take? I declare that no accomplishment has substance nearly as great as the road used to achieve it. We are not creatures of destinations. It is the journey that shapes us. Our callused feet, our backs strong from carrying the weight of our travels, our eyes open with the fresh delight of experiences lived.”

Brandon Sanderson, The Way of Kings

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